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                <div id="site-name"><a href="../../sphinx_pages/build/html/index.html">Shark machine learning library</a></div>
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<p>A kernel is a positive definite function k(x,y), which can be understood as a generalized scalar product. Kernel methods. like support vector machines or gaussian processes rely on the kernels. </p>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="nested-classes" name="nested-classes"></a>
Classes</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_abstract_kernel_function.html">shark::AbstractKernelFunction&lt; InputTypeT &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Base class of all Kernel functions.  <a href="classshark_1_1_abstract_kernel_function.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_abstract_metric.html">shark::AbstractMetric&lt; InputTypeT &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Base-class for metrics.  <a href="classshark_1_1_abstract_metric.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_a_r_d_kernel_unconstrained.html">shark::ARDKernelUnconstrained&lt; InputType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Automatic relevance detection kernel for unconstrained parameter optimization.  <a href="classshark_1_1_a_r_d_kernel_unconstrained.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_discrete_kernel.html">shark::DiscreteKernel</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Kernel on a finite, discrete space.  <a href="classshark_1_1_discrete_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_gaussian_rbf_kernel.html">shark::GaussianRbfKernel&lt; InputType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Gaussian radial basis function kernel.  <a href="classshark_1_1_gaussian_rbf_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_linear_kernel.html">shark::LinearKernel&lt; InputType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Linear Kernel, parameter free.  <a href="classshark_1_1_linear_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_mkl_kernel.html">shark::MklKernel&lt; InputType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Weighted sum of kernel functions.  <a href="classshark_1_1_mkl_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_model_kernel.html">shark::ModelKernel&lt; InputType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Kernel function that uses a Model as transformation function for another kernel.  <a href="classshark_1_1_model_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_monomial_kernel.html">shark::MonomialKernel&lt; InputType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Monomial kernel. Calculates \( \left\langle x_1, x_2 \right\rangle^m_exponent \).  <a href="classshark_1_1_monomial_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structshark_1_1_multi_task_sample.html">shark::MultiTaskSample&lt; InputTypeT &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Aggregation of input data and task index.  <a href="structshark_1_1_multi_task_sample.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_gaussian_task_kernel.html">shark::GaussianTaskKernel&lt; InputTypeT &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Special "Gaussian-like" kernel function on tasks.  <a href="classshark_1_1_gaussian_task_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_normalized_kernel.html">shark::NormalizedKernel&lt; InputType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Normalized version of a kernel function.  <a href="classshark_1_1_normalized_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_point_set_kernel.html">shark::PointSetKernel&lt; InputType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Normalized version of a kernel function.  <a href="classshark_1_1_point_set_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_polynomial_kernel.html">shark::PolynomialKernel&lt; InputType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Polynomial kernel.  <a href="classshark_1_1_polynomial_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_product_kernel.html">shark::ProductKernel&lt; InputType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Product of kernel functions.  <a href="classshark_1_1_product_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_scaled_kernel.html">shark::ScaledKernel&lt; InputType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Scaled version of a kernel function.  <a href="classshark_1_1_scaled_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classshark_1_1_weighted_sum_kernel.html">shark::WeightedSumKernel&lt; InputType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Weighted sum of kernel functions.  <a href="classshark_1_1_weighted_sum_kernel.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="groups" name="groups"></a>
Modules</h2></td></tr>
<tr class="memitem:group__kerneloptimization" id="r_group__kerneloptimization"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__kerneloptimization.html">Kernel Optimization</a></td></tr>
<tr class="memdesc:group__kerneloptimization"><td class="mdescLeft">&#160;</td><td class="mdescRight">All kinds of objective functions to optimize kernel functions. <br /></td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:ga686904ecf2fd8e7d8c1d6799c403afb9" id="r_ga686904ecf2fd8e7d8c1d6799c403afb9"><td class="memTemplParams" colspan="2">template&lt;typename <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> , typename InputTypeT1 , typename InputTypeT2 &gt; </td></tr>
<tr class="memitem:ga686904ecf2fd8e7d8c1d6799c403afb9"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__kernels.html#ga686904ecf2fd8e7d8c1d6799c403afb9">shark::evalSkipMissingFeatures</a> (const <a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; &amp;kernelFunction, const InputTypeT1 &amp;inputA, const InputTypeT2 &amp;inputB)</td></tr>
<tr class="separator:ga686904ecf2fd8e7d8c1d6799c403afb9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga42e81553c9f2aab48ba4a8a3ae37fe6c" id="r_ga42e81553c9f2aab48ba4a8a3ae37fe6c"><td class="memTemplParams" colspan="2">template&lt;typename <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> , typename InputTypeT1 , typename InputTypeT2 , typename InputTypeT3 &gt; </td></tr>
<tr class="memitem:ga42e81553c9f2aab48ba4a8a3ae37fe6c"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__kernels.html#ga42e81553c9f2aab48ba4a8a3ae37fe6c">shark::evalSkipMissingFeatures</a> (const <a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; &amp;kernelFunction, const InputTypeT1 &amp;inputA, const InputTypeT2 &amp;inputB, InputTypeT3 const &amp;missingness)</td></tr>
<tr class="separator:ga42e81553c9f2aab48ba4a8a3ae37fe6c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga3eaca71bfc1467b79c9341dcfcad25c1" id="r_ga3eaca71bfc1467b79c9341dcfcad25c1"><td class="memTemplParams" colspan="2">template&lt;class <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> , class M , class Device &gt; </td></tr>
<tr class="memitem:ga3eaca71bfc1467b79c9341dcfcad25c1"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__kernels.html#ga3eaca71bfc1467b79c9341dcfcad25c1">shark::calculateRegularizedKernelMatrix</a> (<a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt;const &amp;kernel, <a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;dataset, blas::matrix_expression&lt; M, Device &gt; &amp;matrix, double regularizer=0)</td></tr>
<tr class="memdesc:ga3eaca71bfc1467b79c9341dcfcad25c1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculates the regularized kernel gram matrix of the points stored inside a dataset.  <br /></td></tr>
<tr class="separator:ga3eaca71bfc1467b79c9341dcfcad25c1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga3fafbf415f6fec4d166ade39dccbc01a" id="r_ga3fafbf415f6fec4d166ade39dccbc01a"><td class="memTemplParams" colspan="2">template&lt;class <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> , class M , class Device &gt; </td></tr>
<tr class="memitem:ga3fafbf415f6fec4d166ade39dccbc01a"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__kernels.html#ga3fafbf415f6fec4d166ade39dccbc01a">shark::calculateMixedKernelMatrix</a> (<a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt;const &amp;kernel, <a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;dataset1, <a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;dataset2, blas::matrix_expression&lt; M, Device &gt; &amp;matrix)</td></tr>
<tr class="memdesc:ga3fafbf415f6fec4d166ade39dccbc01a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculates the kernel gram matrix between two data sets.  <br /></td></tr>
<tr class="separator:ga3fafbf415f6fec4d166ade39dccbc01a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gabfe57330fd12701e94f030ff1e042ae7" id="r_gabfe57330fd12701e94f030ff1e042ae7"><td class="memTemplParams" colspan="2">template&lt;class <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; </td></tr>
<tr class="memitem:gabfe57330fd12701e94f030ff1e042ae7"><td class="memTemplItemLeft" align="right" valign="top">RealMatrix&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__kernels.html#gabfe57330fd12701e94f030ff1e042ae7">shark::calculateRegularizedKernelMatrix</a> (<a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt;const &amp;kernel, <a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;dataset, double regularizer=0)</td></tr>
<tr class="memdesc:gabfe57330fd12701e94f030ff1e042ae7"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculates the regularized kernel gram matrix of the points stored inside a dataset.  <br /></td></tr>
<tr class="separator:gabfe57330fd12701e94f030ff1e042ae7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga547ea94d882f809b7a33c63cdda4dd37" id="r_ga547ea94d882f809b7a33c63cdda4dd37"><td class="memTemplParams" colspan="2">template&lt;class <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; </td></tr>
<tr class="memitem:ga547ea94d882f809b7a33c63cdda4dd37"><td class="memTemplItemLeft" align="right" valign="top">RealMatrix&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__kernels.html#ga547ea94d882f809b7a33c63cdda4dd37">shark::calculateMixedKernelMatrix</a> (<a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt;const &amp;kernel, <a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;dataset1, <a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;dataset2)</td></tr>
<tr class="memdesc:ga547ea94d882f809b7a33c63cdda4dd37"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculates the kernel gram matrix between two data sets.  <br /></td></tr>
<tr class="separator:ga547ea94d882f809b7a33c63cdda4dd37"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gafb6b639ff5daa090b08b13e97e78a7bc" id="r_gafb6b639ff5daa090b08b13e97e78a7bc"><td class="memTemplParams" colspan="2">template&lt;class <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> , class WeightMatrix &gt; </td></tr>
<tr class="memitem:gafb6b639ff5daa090b08b13e97e78a7bc"><td class="memTemplItemLeft" align="right" valign="top">RealVector&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__kernels.html#gafb6b639ff5daa090b08b13e97e78a7bc">shark::calculateKernelMatrixParameterDerivative</a> (<a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;kernel, <a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;dataset, WeightMatrix const &amp;weights)</td></tr>
<tr class="memdesc:gafb6b639ff5daa090b08b13e97e78a7bc"><td class="mdescLeft">&#160;</td><td class="mdescRight">Efficiently calculates the weighted derivative of a Kernel Gram Matrix w.r.t the Kernel Parameters.  <br /></td></tr>
<tr class="separator:gafb6b639ff5daa090b08b13e97e78a7bc"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#gafb6b639ff5daa090b08b13e97e78a7bc">&#9670;&#160;</a></span>calculateKernelMatrixParameterDerivative()</h2>

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<div class="memtemplate">
template&lt;class <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> , class WeightMatrix &gt; </div>
      <table class="memname">
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          <td class="memname">RealVector shark::calculateKernelMatrixParameterDerivative </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;&#160;</td>
          <td class="paramname"><em>kernel</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;&#160;</td>
          <td class="paramname"><em>dataset</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">WeightMatrix const &amp;&#160;</td>
          <td class="paramname"><em>weights</em>&#160;</td>
        </tr>
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          <td></td>
          <td>)</td>
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<p>Efficiently calculates the weighted derivative of a Kernel Gram Matrix w.r.t the Kernel Parameters. </p>
<p>The formula is \(  \sum_i \sum_j w_{ij} k(x_i,x_j)\) where w_ij are the weights of the gradient and x_i x_j are the datapoints defining the gram matrix and k is the kernel. For efficiency it is assumd that w_ij = w_ji. This method is only useful when the whole Kernel Gram Matrix neds to be computed to get the weights w_ij and only computing smaller blocks is not sufficient. </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">kernel</td><td>the kernel for which to calculate the kernel gram matrix </td></tr>
    <tr><td class="paramname">dataset</td><td>the set of points used in the gram matrix </td></tr>
    <tr><td class="paramname">weights</td><td>the weights of the derivative, they must be symmetric! </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the weighted derivative w.r.t the parameters. </dd></dl>

<p class="definition">Definition at line <a class="el" href="_kernel_helpers_8h_source.html#l00186">186</a> of file <a class="el" href="_kernel_helpers_8h_source.html">KernelHelpers.h</a>.</p>

<p class="reference">References <a class="el" href="group__shark__globals.html#ga73034ee5639176b0d45e1059859d0f0a">shark::Data&lt; Type &gt;::batch()</a>, <a class="el" href="namespaceshark.html#af2ab10364feb8a631e0866dcf2f1a4ad">shark::batchSize()</a>, <a class="el" href="classshark_1_1_abstract_kernel_function.html#a9057a4a71b4d28febb171e09bbd22c07">shark::AbstractKernelFunction&lt; InputTypeT &gt;::createState()</a>, <a class="el" href="classshark_1_1_abstract_kernel_function.html#abd10e3815efade90c7f9e2a7cc8bcb6c">shark::AbstractKernelFunction&lt; InputTypeT &gt;::eval()</a>, <a class="el" href="group__shark__globals.html#gabd82edf467b9b82f4b0a1e70fd695311">shark::Data&lt; Type &gt;::numberOfBatches()</a>, <a class="el" href="classshark_1_1_i_parameterizable.html#aed1e8d1d4dbde387e2f6a25141ed3a20">shark::IParameterizable&lt; VectorType &gt;::numberOfParameters()</a>, and <a class="el" href="classshark_1_1_abstract_kernel_function.html#a48557b9834bc06ccb4e005ce441904c8">shark::AbstractKernelFunction&lt; InputTypeT &gt;::weightedParameterDerivative()</a>.</p>

<p class="reference">Referenced by <a class="el" href="classshark_1_1_negative_gaussian_process_evidence.html#a4bbd89a9d2c47ecc601fb23567715b0d">shark::NegativeGaussianProcessEvidence&lt; InputType, OutputType, LabelType &gt;::evalDerivative()</a>, and <a class="el" href="classshark_1_1_radius_margin_quotient.html#a61c0b73eaf10d43b9a1af891fc51dd5f">shark::RadiusMarginQuotient&lt; InputType, CacheType &gt;::evalDerivative()</a>.</p>

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<h2 class="memtitle"><span class="permalink"><a href="#ga547ea94d882f809b7a33c63cdda4dd37">&#9670;&#160;</a></span>calculateMixedKernelMatrix() <span class="overload">[1/2]</span></h2>

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template&lt;class <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; </div>
      <table class="memname">
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          <td class="memname">RealMatrix shark::calculateMixedKernelMatrix </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt;const &amp;&#160;</td>
          <td class="paramname"><em>kernel</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;&#160;</td>
          <td class="paramname"><em>dataset1</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;&#160;</td>
          <td class="paramname"><em>dataset2</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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<p>Calculates the kernel gram matrix between two data sets. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">kernel</td><td>the kernel for which to calculate the kernel gram matrix </td></tr>
    <tr><td class="paramname">dataset1</td><td>the set of points corresponding to rows of the Gram matrix </td></tr>
    <tr><td class="paramname">dataset2</td><td>the set of points corresponding to columns of the Gram matrix </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>matrix the target kernel matrix </dd></dl>

<p class="definition">Definition at line <a class="el" href="_kernel_helpers_8h_source.html#l00163">163</a> of file <a class="el" href="_kernel_helpers_8h_source.html">KernelHelpers.h</a>.</p>

<p class="reference">References <a class="el" href="group__kernels.html#ga3fafbf415f6fec4d166ade39dccbc01a">shark::calculateMixedKernelMatrix()</a>.</p>

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<h2 class="memtitle"><span class="permalink"><a href="#ga3fafbf415f6fec4d166ade39dccbc01a">&#9670;&#160;</a></span>calculateMixedKernelMatrix() <span class="overload">[2/2]</span></h2>

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template&lt;class <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> , class M , class Device &gt; </div>
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          <td class="memname">void shark::calculateMixedKernelMatrix </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt;const &amp;&#160;</td>
          <td class="paramname"><em>kernel</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;&#160;</td>
          <td class="paramname"><em>dataset1</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;&#160;</td>
          <td class="paramname"><em>dataset2</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">blas::matrix_expression&lt; M, Device &gt; &amp;&#160;</td>
          <td class="paramname"><em>matrix</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
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      </table>
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<p>Calculates the kernel gram matrix between two data sets. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">kernel</td><td>the kernel for which to calculate the kernel gram matrix </td></tr>
    <tr><td class="paramname">dataset1</td><td>the set of points corresponding to rows of the Gram matrix </td></tr>
    <tr><td class="paramname">dataset2</td><td>the set of points corresponding to columns of the Gram matrix </td></tr>
    <tr><td class="paramname">matrix</td><td>the target kernel matrix </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="_kernel_helpers_8h_source.html#l00097">97</a> of file <a class="el" href="_kernel_helpers_8h_source.html">KernelHelpers.h</a>.</p>

<p class="reference">References <a class="el" href="group__shark__globals.html#ga73034ee5639176b0d45e1059859d0f0a">shark::Data&lt; Type &gt;::batch()</a>, <a class="el" href="namespaceshark.html#af2ab10364feb8a631e0866dcf2f1a4ad">shark::batchSize()</a>, <a class="el" href="group__shark__globals.html#gabd82edf467b9b82f4b0a1e70fd695311">shark::Data&lt; Type &gt;::numberOfBatches()</a>, <a class="el" href="group__shark__globals.html#ga814e8b0028cc90dd2af69805e8f8a04d">shark::Data&lt; Type &gt;::numberOfElements()</a>, <a class="el" href="_open_m_p_8h.html#a8a63d79e2c3625260e6092d933f21a98">SHARK_PARALLEL_FOR</a>, and <a class="el" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>.</p>

<p class="reference">Referenced by <a class="el" href="group__kernels.html#ga547ea94d882f809b7a33c63cdda4dd37">shark::calculateMixedKernelMatrix()</a>.</p>

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<h2 class="memtitle"><span class="permalink"><a href="#ga3eaca71bfc1467b79c9341dcfcad25c1">&#9670;&#160;</a></span>calculateRegularizedKernelMatrix() <span class="overload">[1/2]</span></h2>

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template&lt;class <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> , class M , class Device &gt; </div>
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          <td class="memname">void shark::calculateRegularizedKernelMatrix </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt;const &amp;&#160;</td>
          <td class="paramname"><em>kernel</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;&#160;</td>
          <td class="paramname"><em>dataset</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">blas::matrix_expression&lt; M, Device &gt; &amp;&#160;</td>
          <td class="paramname"><em>matrix</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double&#160;</td>
          <td class="paramname"><em>regularizer</em> = <code>0</code>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
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<p>Calculates the regularized kernel gram matrix of the points stored inside a dataset. </p>
<p>Regularization is applied by adding the regularizer on the diagonal </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">kernel</td><td>the kernel for which to calculate the kernel gram matrix </td></tr>
    <tr><td class="paramname">dataset</td><td>the set of points used in the gram matrix </td></tr>
    <tr><td class="paramname">matrix</td><td>the target kernel matrix </td></tr>
    <tr><td class="paramname">regularizer</td><td>the regularizer of the matrix which is always &gt;= 0. default is 0. </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="_kernel_helpers_8h_source.html#l00053">53</a> of file <a class="el" href="_kernel_helpers_8h_source.html">KernelHelpers.h</a>.</p>

<p class="reference">References <a class="el" href="group__shark__globals.html#ga73034ee5639176b0d45e1059859d0f0a">shark::Data&lt; Type &gt;::batch()</a>, <a class="el" href="namespaceshark.html#af2ab10364feb8a631e0866dcf2f1a4ad">shark::batchSize()</a>, <a class="el" href="group__shark__globals.html#gabd82edf467b9b82f4b0a1e70fd695311">shark::Data&lt; Type &gt;::numberOfBatches()</a>, <a class="el" href="group__shark__globals.html#ga814e8b0028cc90dd2af69805e8f8a04d">shark::Data&lt; Type &gt;::numberOfElements()</a>, <a class="el" href="_open_m_p_8h.html#a8a63d79e2c3625260e6092d933f21a98">SHARK_PARALLEL_FOR</a>, <a class="el" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>, and <a class="el" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>.</p>

<p class="reference">Referenced by <a class="el" href="group__kernels.html#gabfe57330fd12701e94f030ff1e042ae7">shark::calculateRegularizedKernelMatrix()</a>, <a class="el" href="classshark_1_1_negative_gaussian_process_evidence.html#a9c74a1a22f2496b879cc1683ee15bc86">shark::NegativeGaussianProcessEvidence&lt; InputType, OutputType, LabelType &gt;::eval()</a>, <a class="el" href="classshark_1_1_negative_gaussian_process_evidence.html#a4bbd89a9d2c47ecc601fb23567715b0d">shark::NegativeGaussianProcessEvidence&lt; InputType, OutputType, LabelType &gt;::evalDerivative()</a>, <a class="el" href="namespaceshark.html#a568356ff4d6d42f5c11402e9cac7d8aa">shark::kMeans()</a>, <a class="el" href="classshark_1_1_kernel_matrix.html#ad5365d1a9d11ca1175b6bb35607db6d1">shark::KernelMatrix&lt; InputType, CacheType &gt;::matrix()</a>, and <a class="el" href="classshark_1_1_regularization_network_trainer.html#a0c203b749f48be1b99e679ea666ff0c0">shark::RegularizationNetworkTrainer&lt; InputType &gt;::train()</a>.</p>

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<h2 class="memtitle"><span class="permalink"><a href="#gabfe57330fd12701e94f030ff1e042ae7">&#9670;&#160;</a></span>calculateRegularizedKernelMatrix() <span class="overload">[2/2]</span></h2>

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<div class="memtemplate">
template&lt;class <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; </div>
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          <td class="memname">RealMatrix shark::calculateRegularizedKernelMatrix </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt;const &amp;&#160;</td>
          <td class="paramname"><em>kernel</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classshark_1_1_data.html">Data</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; const &amp;&#160;</td>
          <td class="paramname"><em>dataset</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double&#160;</td>
          <td class="paramname"><em>regularizer</em> = <code>0</code>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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<p>Calculates the regularized kernel gram matrix of the points stored inside a dataset. </p>
<p>Regularization is applied by adding the regularizer on the diagonal </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">kernel</td><td>the kernel for which to calculate the kernel gram matrix </td></tr>
    <tr><td class="paramname">dataset</td><td>the set of points used in the gram matrix </td></tr>
    <tr><td class="paramname">regularizer</td><td>the regularizer of the matrix which is always &gt;= 0. default is 0. </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the kernel gram matrix </dd></dl>

<p class="definition">Definition at line <a class="el" href="_kernel_helpers_8h_source.html#l00144">144</a> of file <a class="el" href="_kernel_helpers_8h_source.html">KernelHelpers.h</a>.</p>

<p class="reference">References <a class="el" href="group__kernels.html#ga3eaca71bfc1467b79c9341dcfcad25c1">shark::calculateRegularizedKernelMatrix()</a>, and <a class="el" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>.</p>

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<h2 class="memtitle"><span class="permalink"><a href="#ga686904ecf2fd8e7d8c1d6799c403afb9">&#9670;&#160;</a></span>evalSkipMissingFeatures() <span class="overload">[1/2]</span></h2>

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template&lt;typename <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> , typename InputTypeT1 , typename InputTypeT2 &gt; </div>
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          <td class="memname">double shark::evalSkipMissingFeatures </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; &amp;&#160;</td>
          <td class="paramname"><em>kernelFunction</em>, </td>
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          <td></td>
          <td class="paramtype">const InputTypeT1 &amp;&#160;</td>
          <td class="paramname"><em>inputA</em>, </td>
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          <td class="paramkey"></td>
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          <td class="paramtype">const InputTypeT2 &amp;&#160;</td>
          <td class="paramname"><em>inputB</em>&#160;</td>
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          <td>)</td>
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<p>Does a kernel function evaluation with Missing features in the inputs </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">kernelFunction</td><td>The kernel function used to do evaluation </td></tr>
    <tr><td class="paramname">inputA</td><td>a input </td></tr>
    <tr><td class="paramname">inputB</td><td>another input</td></tr>
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<p>The kernel k(x,y) is evaluated taking missing features into account. For this it is checked whether a feature of x or y is nan and in this case the corresponding features in <em>inputA</em> and <em>inputB</em> won't be considered. </p>

<p class="definition">Definition at line <a class="el" href="_eval_skip_missing_features_8h_source.html#l00059">59</a> of file <a class="el" href="_eval_skip_missing_features_8h_source.html">EvalSkipMissingFeatures.h</a>.</p>

<p class="reference">References <a class="el" href="classshark_1_1_abstract_kernel_function.html#abd10e3815efade90c7f9e2a7cc8bcb6c">shark::AbstractKernelFunction&lt; InputTypeT &gt;::eval()</a>, <a class="el" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>, <a class="el" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>, and <a class="el" href="classshark_1_1_abstract_kernel_function.html#a225fbad3a0efdac21e4422576de2ce4e">shark::AbstractKernelFunction&lt; InputTypeT &gt;::supportsVariableInputSize()</a>.</p>

<p class="reference">Referenced by <a class="el" href="classshark_1_1_missing_features_kernel_expansion.html#a6673dbc1445ffc3cd0aea0d547487000">shark::MissingFeaturesKernelExpansion&lt; InputType &gt;::computeNorm()</a>, <a class="el" href="classshark_1_1_missing_features_kernel_expansion.html#ad2194899bc2ad060c751e6f15dceb91a">shark::MissingFeaturesKernelExpansion&lt; InputType &gt;::computeNorm()</a>, <a class="el" href="classshark_1_1_example_modified_kernel_matrix.html#a0138d4fa7cfe2cb0d5228581be209e59">shark::ExampleModifiedKernelMatrix&lt; InputType, CacheType &gt;::entry()</a>, and <a class="el" href="classshark_1_1_missing_features_kernel_expansion.html#ad54351526ec5ab5370b56e5a6b5250ed">shark::MissingFeaturesKernelExpansion&lt; InputType &gt;::eval()</a>.</p>

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<h2 class="memtitle"><span class="permalink"><a href="#ga42e81553c9f2aab48ba4a8a3ae37fe6c">&#9670;&#160;</a></span>evalSkipMissingFeatures() <span class="overload">[2/2]</span></h2>

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template&lt;typename <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> , typename InputTypeT1 , typename InputTypeT2 , typename InputTypeT3 &gt; </div>
      <table class="memname">
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          <td class="memname">double shark::evalSkipMissingFeatures </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classshark_1_1_abstract_kernel_function.html">AbstractKernelFunction</a>&lt; <a class="el" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a> &gt; &amp;&#160;</td>
          <td class="paramname"><em>kernelFunction</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const InputTypeT1 &amp;&#160;</td>
          <td class="paramname"><em>inputA</em>, </td>
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        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const InputTypeT2 &amp;&#160;</td>
          <td class="paramname"><em>inputB</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">InputTypeT3 const &amp;&#160;</td>
          <td class="paramname"><em>missingness</em>&#160;</td>
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          <td></td>
          <td>)</td>
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<p>Do kernel function evaluation while Missing features in the inputs </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">kernelFunction</td><td>The kernel function used to do evaluation </td></tr>
    <tr><td class="paramname">inputA</td><td>a input </td></tr>
    <tr><td class="paramname">inputB</td><td>another input </td></tr>
    <tr><td class="paramname">missingness</td><td>used to decide which features in the inputs to take into consideration for the purpose of evaluation. If a feature is NaN, then the corresponding features in <em>inputA</em> and <em>inputB</em> won't be considered. </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="_eval_skip_missing_features_8h_source.html#l00106">106</a> of file <a class="el" href="_eval_skip_missing_features_8h_source.html">EvalSkipMissingFeatures.h</a>.</p>

<p class="reference">References <a class="el" href="classshark_1_1_abstract_kernel_function.html#abd10e3815efade90c7f9e2a7cc8bcb6c">shark::AbstractKernelFunction&lt; InputTypeT &gt;::eval()</a>, <a class="el" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>, <a class="el" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>, and <a class="el" href="classshark_1_1_abstract_kernel_function.html#a225fbad3a0efdac21e4422576de2ce4e">shark::AbstractKernelFunction&lt; InputTypeT &gt;::supportsVariableInputSize()</a>.</p>

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